A variational model describing the nonlinear mode interaction in thin-walled box-section struts under pure axial compression made from a nonlinear material obeying the Ramberg–Osgood law is presented. The formulation combines continuous displacement functions and generalized coordinates, leading to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals the strongly unstable post-buckling response arising from combined geometrical and material nonlinearities during the interactive buckling of the global and local buckling modes—the resulting behaviour being more unstable with decreasing material hardening. A finite element (FE) model is also devised and reveals very similar post-buckling behaviour as highlighted in the variational model. The results compare very well in terms of the mechanical destabilization and the post-buckling deformation, which verifies the analytical model.